Entropy rate defines the predictability of a sequence of random variables and can be used to characterise behaviour in the presence of noise. Despite its use elsewhere, its application to the behavioural predictability of animals is limited to a study of captive rats. Here we consider whether entropy rate can quantify behavioural predictability in a wild primate and whether this is influenced by individual characteristics and environmental variation. We converted 10-minute continuous focal samples (N=1469) from 28 wild, adult vervet monkeys (Chlorocebus pygerythrus) across three troops into behavioural sequences. We then assessed different time intervals to identify which was most effective at detecting changes in behavioural predictability by calculating entropy rate and sequence length for each. We found that sampling behaviour every 30 seconds resulted in maximum variance across sequences. Using a Bayesian linear mixed effects model, while controlling for sequence length, time of day and troop, we found no evidence for the effect of sex (Estimate=-0.01, l-95% CI=-0.05, u-95% CI=0.04) but strong evidence that entropy rate increased with increasing food availability (Estimate= 0.79, l-95% CI=0.53, u-95% CI=1.04). The fact that environmental variation influences behavioural predictability accords with what we know of environmental effects on primate behaviour and points to the efficacy of using behavioural entropy rate as a method of assessing behavioural predictability in the wild.